This is the latest post in a
series
about Bertrand Russell's essay
Why I am not a Christian, in which I run through his various
arguments and show that they either don't apply to classical theism,
or were invalid in the first place. Russell's essay is split into several
topics, the first of which (after his introduction) is to discuss some
philosophical arguments often used in favour of the existence of God. In
the previous essay, I looked at the first of these, his version of the
cosmological argument. Now, I turn to the second, the argument from the
structure of natural law.

Before I start, I ought to clarify a confusion in Russell's terminology.
For the Aristotelian (such as myself), the phrase natural law
refers to a theory of ethics. The idea is that there are certain ethical
principles which can be derived from a secular understanding of nature.
For example, the idea that it is evil to commit murder is a consequence of
the inherent tendencies of living organisms. To commit murder is to
deliberately frustrate those tendencies, and that is the definition of a
moral evil. This is distinguished from divine law, which are those moral
requirements which are only known from specific commandments from God,
for example the commandment to keep the Sabbath holy.

In this section of his essay, however, Russell uses the phrase to mean
something else, namely the laws that govern the motion of matter, namely
what I call the laws of physics. Russell was here referring to an idea,
popular in the early days of the scientific revolution but not so much
today, that the harmony and consistency of the universe as uncovered by
the study of physics in itself is evidence for the existence of God. God
is seen as a divine lawgiver; one cannot have a lawgiver unless there are
laws he has given. Equally, it is argued in the simplest form of this
argument, one cannot have laws without a lawgiver. In
the case of the laws of physics, that lawgiver cannot Itself be bound by
physics. Since physics describes everything within the material universe,
that means that the lawgiver must be immaterial. And we are now, it is
claimed, well on the way to reaching God.

My presentation in the previous paragraph was somewhat too naive.
For example, it relied on an analogy between human laws and physical law,
and arguments by analogy are often weak. So, before moving to the objections,
I will present a more detailed and mature form of the argument.

In theism, God is not only the creator of the universe, but is active in
sustaining it in every detail. This act of sustaining the universe
involves keeping objects in existence, controlling their motion and
movements, and keeping complex beings bound together. But this is, of
course, precisely the area that comes under the purview of physics. Thus,
for the theist, physics is no more and no less than a description of
God's sustaining of the universe. As such, we can expect that the laws of
physics (whatever is meant by that term; and different versions of theism
mean different things) should in some way reflect the nature and character
of God. The argument from natural law in its weak form states that physical
law has the features that we would expect were it a description of God's
general concourse. In its strong form it states that only a description
of God's general concourse could explain why physics takes the form it
does.

There are several directions in which this thought can be taken. The first
is occasionalism, which is to state that God can do anything to anything.
There is no reason for us to expect regularity in the universe -- there is
no reason why a hat should not suddenly turn into a rabbit and hop off
our heads. This implies that a study of physics would be limited; since
most expressions of physics assume an underlying regularity and homogeneity
of nature, and in occasionalism this assumption is invalid; at best only
approximate. Laws of physics would just be our own
description of observed regular conjunctions, but without a connection to
the real world. For those who subscribe to this doctrine, to say that
the universe is regular would put a limitation on God's power, which is,
to them, clearly absurd.

The second direction is deism, which takes the opposite extreme. This
focuses on the rationality of God, and diminishes God's free will
entirely. It is first of all argued that since God has perfect knowledge
of the future, this can only happen if the future is perfectly predictable.
This means that there are distinct laws of nature which can in principle
be used to predict how matter in the universe changes in time. These laws
stand as something of an intermediary between God and created matter.
God is their author, but once formulated they continue to guide matter
indefinitely without further intervention from God. They must exist
because God Himself uses them to predict the future. Since our intellect
is patterned on that of God, we also can understand them, at least
partially, and should seek to do so.
They inherit from God the properties of universality, rationality and
self-consistency, that they are
unchanging in time and space, that no matter is outside their purview
and they show no favouritism to different corpuscles of matter, and,
as already mentioned, they are deterministic in the sense that given
complete knowledge of the universe at one moment in time it is possible
to predict how it would be at each subsequent moment in time. The study
of and attempt to uncover these laws through a combination of careful
experimentation and logical or mathematical reasoning is natural
philosophy, or (as later came to be known), science.

The middle ground is provided by the theistic forms of Aristotelian philosophy.
This states that instead of being a single law of nature, each individual
type of being has its own inherent tendencies to act in certain ways.
When God acts in the universe, He respects these tendencies. Against the
Occasionalist, the Aristotelian theist would argue that this does not limit
the power of God, because God established the tendencies in the first
place. Unlike in deism, there is not a single tendency for each being.
God has the freedom to choose which of these are actualised at any given
moment. Thus the universe need not be deterministic (it could be, but need
not be). Against the objection of the deist, the Aristotelian would say
that God does not know what is to us the future through prediction, but
on account of His timeless nature, where He observes each moment in time
not in succession (as we do) but together. This allows both free will
(both for God and for us), and perfect knowledge of the future (for God,
but not for us). Since these tendencies ultimately come from God, they
inherit certain properties from God: the tendencies themselves are
unchanging in time and space, depending only on the type of being, and
the likelihood for each tendency to be actualised at any given moment is
also unchanging, depending only on the type of being and the external
circumstances. Since this ordering of nature ultimately arises from God's
intellect, and our intellect is in the image of God's, we can gain at
least a partial knowledge of it, and the attempt to do so through
careful experimentation or logical, mathematical and probabilistic reasoning
is known as natural philosophy, or more recently, science.

The ancient Greeks proposed that the universe was fundamentally
mathematical in nature. This idea was adopted by Plato, and thus remained
in the background throughout the Christian era, albeit suppressed by
the non-mathematical Aristotelian physics. The problem was that for a long time nobody
figured out how to apply mathematics to the physical world in a way that
gave useful results. This difficulty was overcome in the fourteenth
century, and a succession of scholars, starting with the likes of
Bradwardine and Buridan, and culminating in de Soto and Galileo. These scholars showed
that physics not only could be understood mathematically, but it should
be understood so. (At the same time, a second, experimental approach to
modern science was developed; Galileo's genius was chiefly to apply the
experimental approach to test the mathematical ideas of the Oxford and
Parisian scholars). The main weakness of these early pioneers (and why
Renaissance scholars such as Francis Bacon could arrogantly dismiss their
efforts) was that they knew insufficient mathematics to fully express the
laws of nature. They had at their disposal Greek geometry, Indian number
theory, and Indian and Greek algebra as systematised and developed by the
Arabs, and that got them a fair distance, but not as far as needed.
Gradually, the mathematicians filled in the missing ingredients: Descartes'
coordinate geometry, and Newton and Leibniz's calculus were enough for
Newton to develop his laws of motion. Since then the achievements of later
mathematicians in group theory, non-Euclidean geometry, topology,
differential geometry, probability and others have all provided crucial
insights which the physicists have built on.

The mechanistic world view, which was developed in the late middle ages
and dominated scientific philosophy until the early twentieth century,
is the combination of the insights of the mathematical physicists and the
deistic idea of the laws of nature. It adds to deism the idea that
there are fundamental building blocks of matter, these corpuscles are
indestructible, and that everything can be explained in terms of the
matter and locomotion of these particles. It is possible to map from
the physical world to an abstract, mathematical and geometrical
representation of it, perform calculations in the representation, and then
map back to the physical world. The true representation is not analogous
but based on an explicit mathematical mapping, thus it carries a
direct and precise link to the real physical world; what happens in the
representation happens in the actual world.

Of course, in addition to the true mathematical representation of the
world, we also have our own attempts to reconstruct it. There is clearly
a difference between the two, and the difference is this. Firstly, our
knowledge of the laws of physics (the mathematical rules that govern the
representation) is only approximate. This, however, can be and is gradually
improved over time. We know a lot of the features the true laws must have,
but some of the details are still a bit fuzzy. But we know (to a large
extent) where that
fuzziness is, and we know how big it is. Secondly, our knowledge of
the location, locomotion and structure of matter is necessarily imprecise
due to experimental uncertainty.
The true model is precise; our model imprecise. This is not such a serious
problem, since the mathematics of probability allows us to treat that
uncertainty in a systematic way. Our knowledge remains linked to reality,
not by the precise mapping of the true theory, but through a probabilistic
mapping. We cannot say that the final answer is precisely this,
but we can limit it to within narrow bounds, and state the probability for
each possible answer given our initial observations and our uncertainty
of the laws of physics.

Thus modern science arose from premises derived in part from deism. Its
success seemed to vindicate those premises, and consequently the deistic
world view. In particular, deisms rivals, such as polytheism, dualism,
classical theism, occasionalism, and even the early forms of atheism could not provide those
assumptions; indeed they led to perspectives that were contrary to the developing
science. This, then, is (with most of the details omitted) the argument
for the existence of God from physical law more or less as it would have
been presented in the sixteenth to eighteenth centuries.

Of course, this early form of the argument, which is claimed to lead to deism,
assumes that pre-quantum physics is correct. The picture needs modification
when it encounters quantum physics, and the argument is, perhaps, weaker
because it loses its historical vindication. In particular, deism is
inconsistent with the indeterminacy of quantum physics. This doesn't
mean that the argument has gone away; there are plenty other philosophies
which incorporate a belief in God, not least the classical theism which
was original philosophical basis used for Christian theology. A modern
form of the argument would attempt to trace back from quantum field theory
to, say, an Aristotelian philosophy, which allows and more naturally fits
in with quantum indeterminacy.

The argument from natural law is now straight-forward to express. Its
theological roots mean that the laws of physics would inherit certain
properties from God. If the laws of physics did not come from God, there
is no reason why they should inherit those properties, such as being
universal in time and space. Indeed, without God there is no reason why
there should be universal laws in the first place. Thus theological
philosophies such as deism or classical theism make
predictions about the nature of those laws, predictions which seem to be
realised; the atheist philosophies make no such predictions (and
stronger forms of this argument would say that they make predictions which
contradict what we observe; however modern atheism takes the existence of
regular, rational, laws independent of God as an unsubstantiated premise).
This means that the existence of God is a far more reasonable explanation
of why the laws of physics are as they are than God's absence. For
example, some atheist presuppositions imply Hume's ludicrous views
on causality, which directly contradict modern physics; therefore those
pre-suppositions are false.

The argument from physical law is thus a compliment to the cosmological
argument. Certain forms of the cosmological argument argue from physical
law to the principle of causality and from there to God; this
argument goes from God via causality to certain properties which any
physical law must satisfy, these properties are subsequently tested
against reality. The argument from physical law is weaker than the
cosmological argument, since the cosmological argument is based on
deduction, so if the premises are true then so is the conclusion, while
the argument from physical law is based on falsification. There is always
the chance that a wholly different set of premises that we haven't yet
thought of could lead to the same conclusion. However, falsification has
served us well as the basis of much of modern science, so we shouldn't
write it off so quickly either.

So that is the argument: how does Russell respond to it?

A great many things we thought of as natural laws are human conventions.
Three feet make a yard even in deepest space.

Atoms are a lot less subject to law than you might think, and such laws
there are are different to what was supposed, being statistical averages.
We do not regard that a roll of a double six comes up one time in thirty
six as evidence for design; design would imply that they came up double
six every time.

That which represents the momentary state of science today might change
tomorrow.

The idea that natural laws imply a law-giver is based on a false
analogy with human laws.

One would have to ask Why those laws and not others?
Theologians say that it was to create the best possible universe --
you would not believe that by looking at it -- but if there was a reason
for God choosing those laws, then that reason is more fundamental than
God and God Himself is subject to law, and you have got nowhere by
including God in the argument.

The arguments used to show the existence of God change their character
as time goes on. They contain definite fallacies, which are exposed.

The first of these responses is a clear straw man. Yes, we use various
conventions (such as three feet make a yard, or the speed of light is
about
three hundred million meters per second) when mapping from physical
reality to the mathematical representation. But the final result we get,
when we map back to physical
reality at the end of the calculation, is independent of these
conventions.
The expression of Physical law is not tied to one set of conventions; it
works for all of them.
Physics provides us with the means to map from one set of conventions to
another, and allows us to perform calculations regardless of which set
of
conventions we choose (as long as we are consistent in our choice). Beneath
the convention dependent surface, there is a more important convention-blind
layer which can be applied to whatever conventions we happen to favour. It
is that more fundamental, convention independent,
expression of physical law which is the focus of this argument. So pointing
out that some aspects of our calculations are convention-dependent is an
irrelevance because this is not denied by those who make the argument.

Next Russell turns to quantum mechanics. Now, Russell has a point here,
in that the form of this argument that he was thinking of was based on
deism, which implied a deterministic universe which is contradicted by
quantum indeterminacy. However, deism is a relatively recent novelty in
Christian thought (by recent I mean less than a thousand years old).
Russell's argument here is thus powerful against the argument from
deism. Deism makes certain predictions about the nature of physics;
those predictions have turned out to be false, therefore deism is false.

But instead, we should turn back to theism. Obviously, we can't take
theism precisely as it originally stood in early Christianity; we need to combine
it with the insights of the mathematical physicists. The early theists
denied that physics was mathematical; but that assumption was taken
from Aristotle's prejudice rather than theism itself. Replace it with
the assumption that physics can be represented mathematically, and
keep the theism. See where that takes us. Once we have done
so, we can develop a new physical law argument based on those premises,
an argument which is, if anything, closer to the spirit of
Christianity as originally formulated. This understanding does not
require that physics is deterministic, indeed, given God's free will,
it works best with an indeterminate physics. So we expect laws of
nature that are unchanging in time and space, not coordinate system
or convention dependent, rational in that nothing emerges from
nothing, and indeterminate in the sense that particles have several
distinct decay channels, but we cannot predict which of them will be
actualised. The result is in remarkable agreement with modern quantum
field theory. I can't go into details in this post, but I do present
this argument in full detail in chapter 15 of
this book.

When we roll two die, that they come up double six one time in thirty
six is a feature of the design of the dice. The dice has certain
symmetries, and a limited and known number of possible results. The
indeterminacy arises from our lack of knowledge of the initial conditions.
(Quantum indeterminacy is, however, more fundamental).
These features allow us
-- given various other assumptions -- to compute the probability of
each possible outcome. That it is governed by a probabilistic law does
not mean that it is not governed by any law. If it were governed by
no law, then if we rolled the dice, then we could roll a pair of sevens,
or one of them could turn into a rabbit
and the other a bunch of flowers. That that does not happen -- cannot happen
since it violates the conservation of energy and momentum -- implies
that the dice is subject to law. Laws do not need to be deterministic,
and given God's freedom a classical theist would not expect physical law to be
deterministic.

Next, Russell argues that our knowledge of physical law is incomplete.
That is still true, though less so than in his day. But what of it?
Science works by falsification. That means that although we cannot be
certain that what we have is the final answer (we can be sure that what
we have now isn't the final answer), we can be sure that the final
answer will not be certain things. As a corollary, we can describe
certain features that we know the final answer will have. The basic
principles derived from theism are among these. I do not think that we
can, from classical theism, show that there are three families of
particles or whether or not supersymmetric partners exist and a host of
other things, but a lot of the symmetries and structure which sit behind
the modern expressions of physical law emerge from classical theism. Those symmetries are
firmly established. If they were broken, then that would imply
consequences which would have been observed. As we refine our
understanding of physical law, that will allow us to refine the precise
details of the theism which sits at its base (if the argument from
physical law is correct), just as we switch from deism to theism when we
move from classical to quantum physics. This is no different than what
the scientist does in refining their theories in the light of new
evidence. But the basic features of physical law implied by theism (and
in the stronger forms of the argument contrary to atheism) are so
established that they are not going to be changed. New findings in physics
lead to a fine tuning of the theology, not its overthrow.

Some forms of the argument from natural law are based on analogy.
Arguments from analogy are invariably weak -- one has to show that
the features the example has in common with the real object of study
are those very features under consideration; that none of the
differences are of importance. However, not every form of this argument
arises from analogy; in particular not the detailed form I gave above.
Therefore this objection fails to answer all forms of the argument from
natural law, and certainly not the one I present.

Not every theologian depends on ideas of this being the best
possible world, though some have, perhaps most notably Leibniz. Why this
world and not others? To a certain extent, that is answerable, and to
a certain extent it is unanswerable. The argument is not that given
God, we must get precisely this form of physics; but rather we must get
one of a certain subset of possible physical theories. Which of those
theories God selects is entirely God's free choice. If we suppose that
God had certain purposes in creation (such as that a species of rational
animals might emerge), then the constraints that places on the
fundamental physical constants becomes very restrictive, but God still
has some choice.

There is thus a middle ground between saying that God must produce
this particular physics (which might make God subject to the sort of
Law that Russell has in mind) and that we can say nothing about the
type of physics that would describe God's sustaining of the universe
(which would invalidate the argument from natural law). We say that
we can deduce the nature of physics in part but not completely from
our knowledge of God. That partial knowledge is enough to establish
an argument from natural law; that it is not complete invalidates
Russell's objection.

Furthermore, the laws of physics, which we are interested in,
describe the evolution of matter; how God sustains the material
universe. Any law describing God would be of a very different nature,
since God is not material. Thus Russell's objection relies on a false
analogy between the two.

Finally, the argument from physical law does not say that
physics is linked to God by some law which God is bound by. Rather, it
states that God is the origin of physical law, which is constrained
by the nature of God. We can describe that nature, through either
revelation or philosophical reasoning, but such descriptions do not
make God bound to a law which consequently needs to be explained.
Rather, God and His nature is the terminus of all explanations.

Theistic arguments are tested by time and found wanting? Rather, it is
the atheist arguments which have increasingly found to be build on
fallacy. But I can only dispense with them one at a time.

I have not in this post shown that the argument from physical law is valid.
That takes an entire book, and I have
only scratched the surface of a possible modern presentation of the argument
in my work. But what I hope to have
shown in this post is that the arguments raised by Russell in response to
the argument are invalid. It needs a closer look than most contemporary people have
given it.

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